Clifford Algebras with Induced (Semi)-Riemannian Structures and Their Compactifications

Identifying the Clifford algebra Cl r,s with the semi-Riemannian manifold \(\mathbb{R}^{p,q}\), one is afforded an opportunity to examine the conformal geometry of the associated compact manifold, in a manner similar to the case of the Riemann sphere in complex analysis. In this work we consider some low-dimensional examples and provide conjectures to inspire further research.